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This conversation happened in English, which is the second language of the participants. We can see this through the background information and also from the way people use the language (we will explore in later parts). Since this is a written conversation on a forum, word use and context are the only cues we can use to analyze the conversation. Even though English is not their first language, the participants tried to be "polite" through the language markers. Click on the next "i" button for more information
“Politeness is a pragmatic phenomenon by means of which language users express that they take others’ feelings into account and follow the social norms holding for a context” 
Highlighted words are the "politeness markers" in English. They could be the address system like "please", "thank you" & indirect ways to express an urge (can you). In turn 2, B thanked A for the proposal, this expressed B's appreciation for A's effort on the proposal before coming up with other comments. A also thanked B for letting her know of an error (that the budget was not included) by commenting. Both acknowledged each other's opinions & efforts before going to the main message. This indicates that both A and B approached the conversation in a polite manner, as Kadar & House (2021) described: 
In turn 4, B commented on the proposal after A had updated the budget. He believed that too much money was spent on an item related to the T-shirt proposal. B believed the proposal was not strong in funding allocation. However, the way B used words like "is not reasonable", "without fairly distribution" threatens the face of the proposers and could be perceived that B is being impolite by saying things directly. Politeness has two-dimensional phenomenon, described by Spencer Oatey (2005) as “subjective judgements people make about the social (in-) appropriateness of verbal and non-verbal behaviour”. While B "produces" the content, A and C "evaluate" if it was polite to them, which affects how they responded to the comments.
Face is "The public self-image that every competent member of a society wants to claim for themselves"
(Brown & Levinson, 1987)
C, one of the proposers, tried to defend their proposal by addressing B as a "boy". By calling B "boy", C has:
- Denied B's identity as a moderator who is working with her in a professional context.
- Assigned for B the identity of a "boy", which could be associated with young, inexperience, and lack of knowledge to judge the proposal, which B didn't want to claim for himself

Goffman (1967) described "face" as an image of self & its approved social attributes. It is not something inherent in the person but performed in the context. In real life, B has multiple "faces", he could be a 23-year-old man, a child to his family, a friendly friend to his classmate or even a professional moderator at work. B built his "faces" for different contexts and wanted the attributes of those faces to be approved by others. C's actions offended B by causing B to lose his face, this could signal B to "evaluate" that C is being impolite, thus escalating the conversation

Another way to look at this is that: C's first language is not English (evident from the translation tool she used to quote B's comment). So she just wanted to address B by using the word "boy" to indicate B's gender. However, C used 2 questions at the same time, it could cause offense in a normal conversation where the adjacency pair of question-answer is not followed. In the forum context, it is somehow acceptable because users can deliver all the messages they have so the other person will answer it accordingly. The moral order or the standard of behavior in this context (Spencer-Oatey & Kádár, 2016) of a forum implies that it may not be enough to conclude that C is being impolite to B in turn 5 with 2 questions and the address term "boy" (English is not her first language). However, the fact that C messaged 3 turns in a row (5,6,7) without waiting for a reply indicates that she has a lot to say and perhaps is angry. 
In turn 6, C quoted the description of councils' work and said that maybe B was making a mistake. It is interesting to see the clues of impoliteness and politeness in C's comment at the same time. On the one hand, C threatens B's positive face (Brown & Levinson, 1987) by saying that B is making a mistake or being unfair. On the other hand, some of C's words are negative politeness (Cameroon, 2001, p.80) such as: "could you correct me", "I would sincerely appreciate it if you could enlighten me". C didn't impose on B to do anything, but through the way she used the language, she is being polite, and passive-aggressive at the same time. It varies in different cultures of how people express themselves, and it is important to consider how B perceives C's comment to reply her.
In turn 8, many clues suggest that B perceived C's comments as impolite and offensive.
B, in turn, showed a negative evaluation of C's positive face. By saying that C took things personally and inviting her to be mutual respect, B implied that C is being unrespect and using inappropriate language. B showed that he didn't care about C's positive face and even mentioned the taboo topic of C's traits. B again did the Face Threatening Acts (FTAs) mentioned by Brown & Levinson (1987). For example, "Don't take it personal by using such language" is a FTAs, on record, without redressive action & baldly (see diagram 1). It is easy for C to realize that B is doing a FTA to her directly. This is only one of the examples, we can see participants constantly doing the FTAs to each other from the beginning of the forum thread. 
B used a question to answer C's question. This didn't follow the adjacency pair of question-answer and leaves room for C to interpret B's meaning. It could be understood that B didn't want to directly answer the question because it's something obvious and C is asking a redundant question. This violated Grice (1975) conversational maxims of "relevant" and "manner" and is an off-record strategy of politeness. To be more specific, the question is about B's responsibility to read the proposal and he could have answered yes or no. However, answering directly both ways could make B lose face: If the answer is no, it's obvious that B will lose his positive face because he admits he didn't read the proposal. If the answer is yes, B will also lose his negative face because he "had to" answer an obvious question about his responsibility, making him feel C is being superior to him. Because of that, B asked C again another question to answer C's question.

Since the conversation had changed its direction from the proposal to B's responsibilities and C didn't get the reply she wanted, it became more tensed
Due to time limitations, the following messages are to provide clearer context of the conversation. We have gone through an analysis of politeness in forum conversations by looking at written language cues. There are many other cues that could have been analyzed deeper in the conversation, the ones that have been covered are typical cues that we can refer to understand how (im)politeness could be produced and perceived in forum conversation. 

Context of DAO and forum plays an important role in creating a "culture" that shapes how participants interact. We will discuss this further in the next page.
The proposal ended up being rejected
Impoliteness is a phenomenon by means of which language users cause offence
(Kadar & House 2021)
Do the FTA
On record
4. Off record
1. Without redressive action, baldly
With redressive action
2. Positive politeness
3. Negative politeness
5. Don't do the FTA

Politeness strategies (Brown & Levinson 1987)

Diagram 1